Rainfall-runoff relationship, factors affecting runoff

Rainfall-runoff relationship for a large catchment

For a large catchment, runoff $R$ (depth, cm) depends on rainfall $P$ (cm) mainly through losses. Relations are established from records of the catchment, as follows.

1. Correlation (regression) method

• Collect annual or seasonal values of $P$ (catchment average rainfall by Thiessen or isohyetal method) and the corresponding $R$ (observed flow converted to depth).
• Plot $R$ against $P$; fit a straight line by least squares:

$$R = aP + b$$

where $a=\dfrac{N\sum PR-\sum P\sum R}{N\sum P^2-(\sum P)^2}$ and $b=\bar R - a\bar P$. A correlation coefficient $r$ near 1 shows a reliable relation.

• Where the relation is curved, use $R = aP^{n}$ or a polynomial.

 R |            . . /
   |        . . /
   |     .  /      best-fit line
   |   . /
   | /
   +----------------- P

2. Runoff coefficient: $R = CP$ (or $Q_p=CiA/360$ for peak flow), where $C$ depends on land use, soil and slope.

3. Khosla's formula (monthly): $R_m = P_m - L_m$, with loss $L_m = 0.48T_m$ (cm) for mean temperature $T_m>4.5\ ^\circ$C.

4. SCS curve-number method (storm):

$$R=\frac{(P-0.2S)^2}{P+0.8S},\qquad S=\frac{25400}{CN}-254\ \text{(mm)}$$

Factors affecting runoff from a basin

• Climatic: rainfall intensity, duration, distribution, antecedent moisture, storm movement, evaporation, temperature.
• Catchment: size, shape, slope, land use and vegetation, soil type and geology, drainage density, depression and lake storage.
• Channel: cross-section, roughness and slope.
• Human: dams, diversions, urbanisation, irrigation.

The larger the catchment, the lower the specific runoff from short storms because of storage and attenuation.